Asymptotic expansions of symmetric standard elliptic integrals

Symmetric standard elliptic integrals are considered when one of their para meters is larger than the others. The distributional approach is used for d eriving five convergent expansions of these integrals in inverse powers of the respective ve possible asymptotic parameters. Four of these expansions also involve a logarithmic term in the asymptotic variable. Coefficients of these expansions are obtained by recurrence. For the first four expansions these coefficients are expressed in terms of elementary functions, whereas coefficients of the fifth expansion involve nonelementary functions. The c onvergence speed of any of these expansions increases for increasing differ ence between the asymptotic variable and the remaining ones. All the expans ions are accompanied by an error bound at any order of the approximation.